As further evidence for this idea, in the introduction of [1]} de Cataldo and Migliorini noted that the perverse Leray filtration and the action of cup product display a “striking similarity with the structures discovered on the cohomology of the limit fiber... in the case of degenerating families along a normal crossing divisor, where the logarithms of the monodromies, instead of the cup products with Chern classes of line bundles, are the endomorphisms giving the filtrations”. We claim that this similarity is, in fact, a manifestation of mirror symmetry.
